Robs you done well there I rekon.
The LP12 although fashionable to bash on these forums does represent great VFM when you get it cheap.
Before he sends it request that the thrust plate and platter are removed, this is essential becuase if the thrust plate gets knocked in transit you will have a dead ducky.
Once its in your humble abode you can check it out. As with all decks it needs to be very level. However there are three distinct areas to the LP12 which always give different reading on level. I typically insure that the platter is smack on, and that the arm plate is dead level with the deck, this gives the best average.
Firstly put the thrust plate in, insuring there is sufficent oil, then place the platter on upside down. Start her up and you can see under to check the moters turning properly , that there is no slippage in the belt etc. Stop her and remove the platter and put it on correctly, check for bounce, by knocink the arm plate (Obviously we arn't playing records at this point!) If there is little bounce then the springs might want turning, this will also correct the arm board if its twisted.
Word of warning if it has a valhalla board underneath unplug it before attempting to turn the springs as you will get a nasty jolt (I have done this!) turning the springs is just that, you need access from underneath for this, turn them until you get a nice bounce and the arm board is straight. If it dips anywhere you can tightnen or loosing the offending spring.
As for the arm, well use it for now but I would get shot as soon as, mabye an RB300 will be better suited, also check the cart. In this area it would be well worth spending a few bob on a decent MM, as the one on it might well be knankered and will ruin your records.
Finnaly as for cleaning. well the main metal plate is a bitch. Clean with a soft yellow scourer (Such as a tescos value one) warm water and washing up liquid. Once dried apply the tiniest amount of baby oil to the surface to stop it blotching up, when I say tiny I mean it.
The platter if in original condition will be dull, leave it this way, do not be tempted to brasso it like I did as you have to polish the bloody thing every week. The wood on the outside I reccomend a product called Wheelers Tradional Beeswax Dark Furniture Cream, available from trewins, John Lewis, its only a couple of quid but brings the wood up a treat.
Manuals are avilable on line for the linn deck, i'll have a dig around.
